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I have a background in statistics and was interested in learning more about modeling with Stochastic Differential Equations. I understand the basics of stochastic processes and measure theory, etc., as well as differential equations and numerical methods. I started to read Evan's short guide to SDEs which is nice. But I find myself getting a bit lost in a lot of the formalisms for defining martingales and then brownian motion, etc. I tend to find it hard to simply read equations instead of seeing someone explain the derivations--especially for a new topic.

I was hoping someone could recommend some online videos or online course on Stochastic Differential Equations. I found a lot of videos on Youtube and google, but was not sure which of them are good. Many of those videos are very incomplete, etc. Any help would be appreciated.

Thanks.

krishnab
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    Ceterum censeo: ask for videos at youtube, ask for mathematics, here. –  Dec 15 '20 at 15:31
  • yep, a video is a lot more incomplete that any (possibly small) book on the subject, so... – Masacroso Dec 15 '20 at 15:35
  • @Masacroso I suppose there is a balance between books and videos. I compare it to trying to understand a painting. If I look at a painting from 2 inches away, I can see all th detailed strokes and color gradations, but I can't figure out what the objects are. That is like a book which provides all of the formal details. If I stand 6 feet from the painting, now I have an adequate high level understanding of the objects, and am ready to investigate the more minute details. So I find that going back and forth between high and low levels of details helps. – krishnab Dec 15 '20 at 15:54
  • @ProfessorVector i appreciate your viewpoint, but there are other questions on this site that solicit book and video recommendations. For example: https://math.stackexchange.com/questions/140126/is-there-any-good-resource-for-video-lectures-of-differential-geometry – krishnab Dec 15 '20 at 15:56
  • @ProfessorVector, Youtube isn't a question-and-answer site--- not even close. You may as well tell him his question is dumb. (Also, people regularly ask for book recommendations here... should they go to Amazon?) –  Dec 16 '20 at 16:10

2 Answers2

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Maybe this answer is a bit late for you but I am sure there are a lot of other people with the same question. To them, I recommend the following:

  1. Stochastic Processes - University of Leipzig
  2. Stochastic Analysis and Stochastic Differential Equations - University of Oslo
  3. Stochastics II - Freie Universität Berlin
  4. Stochastic Partial Differential Equations - Freie Universität Berlin
Siddhartha
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  • As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. – Community Nov 03 '21 at 09:14
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    @Siddhartha these are some excellent suggestions. I just looked at the University of Oslo one, but seem very informative. Thanks for posting these suggestions. – krishnab Nov 03 '21 at 17:05
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I did find this set of videos very helpful. They are by MIT with a financial focus, but the lectures by Choongbum Lee were at the right level of formalism versus intuition for me. He does a good job of explaining

https://www.youtube.com/playlist?list=PLUl4u3cNGP63ctJIEC1UnZ0btsphnnoHR

In lecture 5, Lee goes over the basics of stochastic processes. Then the real materials starts in lecture 17 where he goes over continuous time processes and derives Ito's Lemma. Lecture 18 continues with Ito's lemma, integration of the Ito integral, and finally a discussion on Girsanov's theorem.

After watching these videos I feel a lot more comfortable reading Evan's book on SDEs or Kloeden, etc.

krishnab
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